Agreed. I whinge about this all the time. The C-based system is convenient for piano players but it's a mess for guitar players, violinists, and other instruments where there are no
There have been many attempts at a chromatic music notation, but nothing has caught on so far [1].
Things are a little better with solfege -- there is "chromatic fixed do" solfege, where every note has its own name, rather than only having a name for the "white notes," which leaves you to mentally calculate the sharps and flats.
It's a minority thing--maybe 5-10% in Europe? Even regular fixed "do" is rare in English-speaking countries, so I would assume the chromatic fixed "do" is almost unheard of in the US, Britain, etc.
At any rate, there're are at least seeds of hope for a chromatic fixed-do solfege to catch on more. I use it for my own learning.